That should only happen if you change the account a second time.
That is, if you currently have your new Apple Account logged in (and have not already changed accounts on this device), you can log in to the old one without waiting. If you then log out of the old one, then you need to wait 90 days before you can log in with the new one again.
If you already changed accounts once, then yes, you would need to wait 90 days before you can log in again with the other account.
This is why you should only use one Apple account on a device. It gets complicated and cumbersome when you have more than one account.
If this is a work device, then keep the work account. If this is a personal device, then use the personal account.
Creating additional accounts just complicates things.
If you need to add an account to family sharing then the organizer can invite the account to the group if the group still has space for it (Less than 6 total accounts are part of family sharing).
If the group already has 6 accounts added, then the organizer can remove one account from the group and then invite the other one.
This should have no effect on the 90 days limitation of logging in to accounts.
Do note though, that if an account has been part of 2 family groups within a single year, it cannot join another Family group or rejoin the previous family group for a year.
click here ➜ Set up Family Sharing - Apple Support